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# A vegetable vendor purchased 140 kg of tomatoes from the market at the rate of X per kg. 15% of the tomatoes got perished during transportation. He sold the remaining tomatoes at a per kg rate of 25% more than X. If he made a profit of 560, find the value of X

To find the value of X, we can follow these steps:

1. Calculate the weight of tomatoes that got perished.
2. Calculate the weight of tomatoes that were left to sell.
3. Calculate the cost price of the remaining tomatoes.
4. Calculate the selling price of the remaining tomatoes using the profit made.
5. Calculate the per kg selling price of the remaining tomatoes.
6. Calculate the per kg cost price of the tomatoes (X).

Let’s go through these steps:

1. Calculate the weight of tomatoes that got perished:

Weight_Perished = Total_Weight_Tomatoes * Perished_Percentage Weight_Perished = 140 kg * (15/100) Weight_Perished = 21 kg

1. Calculate the weight of tomatoes that were left to sell:

Weight_Left = Total_Weight_Tomatoes – Weight_Perished Weight_Left = 140 kg – 21 kg Weight_Left = 119 kg

1. Calculate the cost price of the remaining tomatoes:

Cost_Price_Remaining_Tomatoes = Weight_Left * X Cost_Price_Remaining_Tomatoes = 119 kg * X

1. Calculate the selling price of the remaining tomatoes using the profit made:

Selling_Price_Remaining_Tomatoes = Cost_Price_Remaining_Tomatoes + Profit Selling_Price_Remaining_Tomatoes = 119 kg * X + 560

1. Calculate the per kg selling price of the remaining tomatoes:

Per_Kg_Selling_Price = (119 kg * X + 560) / 119 kg

1. Calculate the per kg cost price of the tomatoes (X):

Since the vendor sold the remaining tomatoes at a per kg rate of 25% more than X:

Per_Kg_Selling_Price = X + 0.25 * X Per_Kg_Selling_Price = 1.25 * X

Now, we can equate the expressions for the per kg selling price and solve for X:

1.25 * X = (119 kg * X + 560) / 119 kg

Multiplying both sides by 119 kg to eliminate the denominator:

1.25 * X * 119 kg = 119 kg * X + 560

Simplifying further:

148.75 * X = 119 * X + 560

Subtracting 119 * X from both sides:

29.75 * X = 560

Dividing both sides by 29.75:

X = 560 / 29.75 X ≈ 18.82

So, the value of X is approximately 18.82

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